27% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two (b) more than two (c) between two and five inclusive. If convenient, use technology to find the probabilities. (a) P (2) = (round to the nearest thousandth) (b) P (x>2) = (round to the nearest thousandth) (c) P (2 < = x < = 5) = (round to the nearest thousandth)

Question

Mathematics

Goblin

17 March, 05:04

27% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two (b) more than two (c) between two and five inclusive. If convenient, use technology to find the probabilities. (a) P (2) = (round to the nearest thousandth) (b) P (x>2) = (round to the nearest thousandth) (c) P (2 < = x < = 5) = (round to the nearest thousandth)

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Answers (1)

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Adan Krause · Answer 1

a) P (2) = 0.2646

b) P (x > 2) = 0.5334

c) P (2 < = x < = 5) = 0.7694

Step-by-step explanation:

n = 10

p = 0.27

q = 0.73

x = 10

P (x=0) = (10 C 0) (0.27^0) (0.73^ (10-0)) = 0.043

P (x=1) = (10 C 1) (0.27^1) (0.73^ (10-1)) = 0.159

P (x=2) = 0.2646

P (x=3) = 0.2609

P (x=4) = 0.1689

P (x=5) = 0.075

P (x=6) = 0.0231

P (x=7) = 0.0049

P (x=8) = 0.000677

P (x=9) = 0.0000557

P (x=10) = 0.00000206

a) P (2) = 0.2646

b) P (x > 2) = P (3) + P (4) + P (5) + ... + P (10) = 0.5334

c) P (2 < = x < = 5) = P (2) + P (3) + P (4) + P (5) = 0.7694